proof ch:10-hilbert-spaces@proof-19

open in the book · parts/02-mathematical-methods/10-hilbert-spaces.tex:929

Rests on

No declared or derived dependency edges point away from this node yet.

Supports

Nothing declares a dependency on this node yet.

Neighborhood

Every logical edge within two steps of this node.

proof : ch:10-hilbert-spaces@proof-19proofproposition 12.37: B(H) is a Banach algebra12.37definition 12.35: Bounded operator; operator norm12.35proposition 12.8: Absolutely convergent series test12.8lemma A.240: Spectral mapping for polynomialsA.240proposition 12.65: Exponential of a bounded self-adjoint operator12.65proposition 12.61: Uniqueness of the continuous functional calculus12.61proposition 12.39: Algebra of the adjoint; the C^\ast identity12.39proposition 12.52: Neumann series; the spectrum is bounded12.52theorem 12.38: Existence and uniqueness of the adjoint12.38theorem 12.75: The canonical commutation relation admits no bounded solution12.75

Edges

typedirectionnode provenancewhere
proves $\mathcal{B}(\mathcal{H})$ is a Banach algebra declared parts/02-mathematical-methods/10-hilbert-spaces.tex:929